# FFT and number of samples relations

I am new in signal processing. I generated a signal with $f_{in}=10 \mathrm{kHz}$ and also take 64 sample from this signal after doing some process in an ADC block. I want to convert the result to the main signal and compare them whit each other. So if what is the difference between taking an FFT of the 64 points or other numbers like 1024 in the same measured time and what should be changed?

Thank you

## 1 Answer

It is not clear from your question why you are even taking an FFT; knowing that may also lead to additional insights- but the main point to understand is frequency resolution in the FFT; assuming you are not doing any windowing (shaping the envelope of the time domain signal before taking the FFT), the frequency resolution is 1/T where T is the length of your FFT block in seconds. From this you will see that the frequency resolution is one FFT bin, and is equal to $f_s/N$ where $f_s$ is the sampling rate used and N is the number of samples in the FFT.

For additional info on this see What happens when N increases in N-point DFT and the additional referenced posts there.

• Thank you for the answer, I want to test my ADC (Analog to Digital) circuit design. So I generated an input wave with fin=10 kHz then I took 64 samples from it, after processing with the circuit I have digital codes that I should convert them back to continues time by ideal block, by using ideal DAC (Digital to Analog Converter). I want to examine the accuracy of the ADC, so I should take an FFT with the 64, 128,.. points. I really don't know I should have 64 samples in the input of ADC or more for other numbers of FFT calculation like 128 points, ... – saleh May 16 '17 at 22:03
• why take an FFT? why not just take the difference and get the rms of the error signal? – Dan Boschen May 17 '17 at 2:49
• I appreciate the time that you dedicated to answering. I have a formula that should be used in it, SNR and THD ( Total harmonic distortion). By taking FFT and finding THD I could find SNR and from this, I can find the effective resolution of the ADC. I don't know exactly by using the difference with something that you said, maybe I could find my answer but I am not sure without comparing with the true answer. – saleh May 17 '17 at 22:16
• Yes taking the error and taking the variance will be equivalent for what you are trying to do but with significantly less processing. The variance of the difference will be the total power across the entire spectrum due to quantization noise and all other noise sources (integral and differential non-linearity etc) in the ADC – Dan Boschen May 17 '17 at 23:05
• If you want the power in just the harmonics then what you describe would be worth while, but if you want the total error signal what I described will get you there quickly. – Dan Boschen May 17 '17 at 23:06